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Given two $k$-uniform hypergraphs $F$ and $G$, we say that $G$ has an$F$-covering if every vertex in $G$ is contained in a copy of $F$. For $1\le i\le k-1$, let $c_i(n,F)$ be the least integer such that every $n$-vertex$k$-uniform hypergraph $G$ with $\delta_i(G)> c_i(n,F)$ has an $F$-covering.The covering problem has been systematically studied by Falgas-Ravry and Zhao[Codegree thresholds for covering 3-uniform hypergraphs, SIAM J. DiscreteMath., 2016]. Last year, Falgas-Ravry, Markstr\"om, and Zhao [Triangle-degreesin graphs and tetrahedron coverings in 3-graphs, Combinatorics, Probability andComputing, 2021] asymptotically determined $c_1(n, F)$ when $F$ is thegeneralized triangle. In this note, we give the exact value of $c_2(n, F)$ andasymptotically determine $c_1(n, F)$ when $F$ is the linear triangle $C_6^3$,where $C_6^3$ is the 3-uniform hypergraph with vertex set$\{v_1,v_2,v_3,v_4,v_5,v_6\}$ and edge set $\{v_1v_2v_3,v_3v_4v_5,v_5v_6v_1\}$.

The degree and codegree threshold for linear triangle covering in 3-graphs